DENVER — Sen. Tom Cotton made no mention Saturday of the Republican presidential ticket, but had plenty to say about the Democratic campaign scandal involving President Bill Clinton’s private airport meeting.

The Arkansas Republican joked that he was stuck on the tarmac in Denver so long that he thought he might be getting a visit from the former Democratic president.

“I was a little worried I might not make it this morning,” Mr. Cotton told the crowd at the Western Conservative Summit. “I flew in, and our plane waited for a long time on the tarmac. We were waiting so long I thought Bill Clinton might be boarding my plane to come to talk to me.”

“But then I realized I’m a mere United States senator. I’m not the Attorney General who will decide whether to indict his wife or not,” said Mr. Cotton.

Mr. Clinton sparked an outcry over disclosures about a private meeting last week at a Phoenix airport with Attorney General Loretta Lynch, which took place even though the Justice Department is investigating his wife Hillary Clinton’s unsecured emails during her tenure as Secretary of State.

Mr. Cotton’s comments came during the seventh-annual summit, billed as the nation’s largest annual gathering of conservatives outside Washington, D.C., sponsored by the Centennial Institute at Colorado Christian University.

“Hillary’s reckless and even criminal disregard for our nation’s secrecy laws and the sensitive handling of classified information in my opinion disqualifies her from being our commander-in-chief,” Mr. Cotton said.

A rising Republican Party star, Mr. Cotton has been mentioned as a possible vice presidential choice for presumptive Republican presidential nominee Donald Trump, who spoke Friday at the conference.

Even so, Mr. Cotton said nothing about Mr. Trump but rather focused his speech on Mrs. Clinton, the all–but-certain Democratic presidential candidate.

“The Democrats had a choice between two socialists, and they chose the one under FBI investigation,” said Mr. Cotton, who sits on the Senate Intelligence Committee.

He said Mrs. Clinton’s latest testimony before the FBI, combined with Mr. Clinton’s meeting with the attorney general, should remind voters of “the kind of casual, carefree, ethics-free zone that comes with the Clintons everywhere they go.”

“And it should be a reminder to the American people of the kind of endless ethics controversies and scandals that we’ll have in store for us if we choose Hillary Clinton as our next president,” said Mr. Cotton.

Ms. Lynch has characterized the meeting with Mr. Clinton as a chance encounter that focused on friendly conversation about his grandchildren and travels, and insisted that there was no discussion of the email investigation.